The positions of two particles on the s-axis are s1 = sin t and s2 = sin (t + pai/3), with s1 and s2 in meters and t in seconds. a. At what time(s) in the interval 0<=t<=2pai  do the particles meet? b. What is the farthest apart that the particles ever get? c. When in the interval 0<=t<=2pai is the distance between the particles changing the fastest?

Q: Let ŕ ). ) - (0**) k (4 Sin 2+) + (4 cos 2 t, be the Position oF Perticle space in at time. Finc the…

A: The velocity is dr/dt and the acceleration is d2r/dt2

Q: Find the length L of the curve R(t) = e* cos(3t) i + e* sin(3t) j + 3e*k over the interval [1, 5]. L…

A: given: Rt=etcos3ti+etsin3tj+3etk interval 1,5

Q: Find the speed at the given value of t. r(t) = (sin(3t), cos(6t), cos(7t)), t = %3D (플) = 프2

A: Given:

Q: Eliminate the paranoter t from the follewing S r(1) = 4+ sin t lu(t) 3- cost

A:

Q: The positions of two particles on the s-axis ares1 = sin t and s2 = sin (t + π/3), with s1 and s2 in…

A:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: the length of the curve r = V1+ cos 20 for – -sos.

A: In this question, the length of the curve is to be determined. Length of Curve The length of the…

Q: Find the length of the following curve: y = ln(cos(x)) from x=0 to x=pi/4

A:

Q: Suppose the position function of a particle is given r(t) = (√3 cos (t), t-4, √3 sin(t)). If the…

A: Given : r(t)=3cos(t), t-4, 3sin(t) is the position function of a particle. To find : If the particle…

Q: Two masses hanging side by side from springs have positionss1 = 2 sin t and s2 = sin 2t,…

A:

Q: Find the speed at t = π/4 of a particle whose position at time tseconds is c(t) = (sin 4t, cos 3t)

A:

Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0 <t< n/4

A:

Q: find the speed at the given value of t. r(t) = (sin 3t, cos 4t, cos 5t), t =

A: Given: rt=sin3t, cos4t, cos5t To find the speed at the given value of t=π2. Solution: Speed is the…

Q: The length of the curve y= In(cosx) between X=0 and X = TT/3 is given by: a. None of the other…

A:

Q: The positions of two particles on the s-axis are s1 = sin t and s2= sin t+- with S1 and s2 in meters…

A: Here we have given the Position of two particles that are S1=Sin(t) and S2=Sin(t+π/2). Where S1 and…

Q: Prove the left side equal to right side in the following: s2 (eice = (sin at + at cos ar] 1 L-1 (s²…

A:

Q: Find the length of the spiral c(t) = (t cos t, t sin t) for 0 <t < 2n to three decimal places. Hint:…

A:

Q: 8. Find the length of the given curve over the indicated interval. r(t)= (r', 3 cos(t), 3t) [] 0, 2

A: Given r¯(t)=t2,3cost,3t in the interval [0,π2]

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: None of the choices…

A:

Q: Find the quadrant in which the point P(t) lies if the following conditions are true. (a) cost > 0…

A:

Q: The approximation of I = , tanx dx using composite Simpson's rule with n=5 is: 0.6158 0.6165 None of…

A:

Q: The area of a triangle is to be computed from the formula A = ½ab sinθ, where a and b are the…

A: Given that, the area of the triangle is determined by A=12absinθ where a, b are two sides and θ is…

Q: r = 2 cos 0,0 <o <n. 2 L = S°. dr r2 + de de.

A: Use the formula given to find length of curve.

Q: A) Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Let C be the curve parameterized by Y: [0, b] R³, y(s) = (12 cos(s²), 12 sin(s), 9 s²). Find b>0…

A: The given problem is to find the value of b for which the given length of curve of the given…

Q: 9. Find the length of the curve: r = 1+ cos(20),0 < 0 s 2n

A: given equation of curve r=1+cos(2θ)   , 0≤θ≤2π as per our guideline, we are supposed to answer the…

Q: A standing wave on a 2-m stretched string is described by: y(x,t) = 0.1 sin(2rtx) cos(50tt), where x…

A: Solution :-

Q: Calculate the length of the path over the given interval. (sin 7t, cos 7t), 0≤t≤n

A:

Q: Find the length of the curve. r(t) = cos(6t) i + sin(6t)j + 6In(cos(t)) k, 0stsa/4

A: In this question we have to find the length of the curve.

Q: For which values of t is the curve concave upward? x=cos(2t) y=cos(t)

A:

Q: Under what conditions for the contants a,b, k,e =) is (aa+by) da + (ka + ly) dy = 0 exact? Solve the…

A:

Q: Find the length of the curve 7 (t) = (4 cos(5t), 4 sin(5t), 5t) for – 3 < t < 9 Give your answer to…

A: Given: r→t =4cos(5t), 4sin(5t), 5t  for -3≤t≤9

Q: To give the first digit x the second digit y, three points are given as follows: (0, 0), (ax, ay),…

A: The given points are as follows: x y ∆y ∆2y 0 0 ay by-2ay ax ay by-ay   bx by…

Q: the wire that lies along the curve Di + (7 sin t)j. 0sts5 Osts1; 8= 5? its

A: We have to find the mass of wire according to the given information

Q: Find the length of the curve. r(t) = cos(5t) i+ sin(5t)j + 5ln(cos(t)) k, 0<t< n/4

A: r(t)=cos(5t)i+sin(5t)j+5ln(cos(t))kWhere, 0≤t≤π/4

Q: At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by M(t) = 3.85(10 – t)² In(t…

A:

Q: 7. Find the length of the curve: r = 1 + cos 0

A:

Q: 10 cos 0 and y = 10 sin³ 0, find the total length of the curve swept out by the point If x = (x, y)…

A: We have to point length of curve swept out by the point:

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: Differentiate x with respect t. dxdt=ddtcos2t=-2sin t cost  Differentiate y with respect to t.…

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A: The objective of the problem is to find the distance traveled by the particle whose position is…

Q: Find the distance traveled by a particle with position (х, у); Cos t, y = (cos t)², 0 < t < 4TT X =

A: To solve this we have to use two point distance formula

Q: Find the distance traveled by a particle with position (x, y) as t varies in the given time…

A:

Q: Find the length L of the curve R(t) = 4 cos(5t) i – 4sin(5t) j + tk over the interval [3, 6]. L =…

A: Given:

Q: T= 8 cos 30. with /met: A =

A:

Q: Find the length of the curve. r(t) = cos(2t) i + sin(2t) j + 2 In(cos(t)) k, osts n/4

A: Given:

Q: Find the exact length of the curve. y = In(cos(x)), 0 s xs- TO 6. Need Help? Read It

A: Given problem:- Find the exact length of the curve.   y = In(cos(x)),   [0, π/6]

Q: If x = 10 cos 0 and y = 10 sin 0, find the total length of the curve swept out by the point (x, y)…

A:

Q: The position of a particle in the xy-plane at time t is given by r(t) = (cos 2t) i+ (2 sin 2t) j…

A: Given: rt=cos2ti+2sin2tj For finding equation in x and y whose graph is the path of the particle, we…

Q: At a bakery, muffins are made from 4 A.M. to 10 A.M. at a rate modeled by M(t) = 3.85(10 – t) In(t –…

A: